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Tanzania [10]
3 years ago
14

Jonah collects rainwater in a large barrel that weighs 30 pounds. When there are 10 gallons of water in the barrel, the total we

ight of the barrel and the water is 113.4 pounds. When there are 20 gallons of water, the total weight is 196.8 pounds. Which equation and graph match this situation? A. y = 8.34x + 30 B. y = 30x + 8.34 C. y = 30x + 8.34 D. y = 8.34x + 30
Mathematics
1 answer:
Serjik [45]3 years ago
8 0
The first thing we are going to do for this case is define variables.
 We have then:
 x: number of gallons of water
 y: total weight
 We then have an equation of the form:
 y-yo = m (x - xo)

 Where,
 m = (y2 - y1) / (x2 - x1)

 Substituting values:
 m = (196.8 - 113.4) / (20 - 10)

m = 8.34
 We choose an ordered pair:
 (xo, yo) = (10, 113.4)

 Substituting values:
 y-113.4 = 8.34 (x - 10)

 Rewriting:
 y = 8.34x - 83.4 + 113.4

y = 8.34x + 30
 Answer:
 
y = 8.34x + 30
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Frozen motts sticks cost $.022 each. If there are 6 sticks in on order, what is the portion cost for an order of motts sticks?
solong [7]

Answer:

$ 1.32

Step-by-step explanation:

<u>Given </u><u>:</u><u>-</u><u> </u>

  • Cost of each Mott's Stick = $0.22 .

Now there are 6 sticks in an order . So the cost of six sticks will be ,

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2 years ago
Suppose the heights of a population of people are normally distributed with a mean of 65.5 inches and a standard deviation of 2.
kupik [55]

Answer:

a) P(64.2

b) 69.764

Step-by-step explanation:

1) Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

2) Part a

Let X the random variable that represent the heights of a population, and for this case we know the distribution for X is given by:

X \sim N(65.5,2.6)

Where \mu=65.5 and \sigma=2.6

We are interested on this probability

P(64.2

And the best way to solve this problem is using the normal standard distribution and the z score given by:

z=\frac{x-\mu}{\sigma}

If we apply this formula to our probability we got this:

P(64.2

And we can find this probability on this way:

P(-0.50

And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.

P(-0.50

3) Part b

For this part we want to find a value a, such that we satisfy this condition:

P(X>a)=0.05   (a)

P(X   (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.

As we can see on the figure attached the z value that satisfy the condition with 0.95 of the area on the left and 0.05 of the area on the right it's z=1.64. On this case P(Z<1.64)=0.95 and P(z>1.64)=0.05

If we use condition (b) from previous we have this:

P(X  

P(z

But we know which value of z satisfy the previous equation so then we can do this:

z=1.64

And if we solve for a we got

a=65.5 +1.64*2.6=69.764

So the value of height that separates the bottom 95% of data from the top 5% is 69.764.

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Answer:

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Step-by-step explanation:

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(If you don't believe me, do it out.)

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